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(A) The pressure $P$ exerted by an ideal gas on the walls of a container is given by the kinetic theory of gases as $P = \frac{1}{3} \rho v_{rms}^{2}$

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$1$

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(A) The pressure $P$ exerted by an ideal gas on the walls of a container is given by the kinetic theory of gases as $P = \frac{1}{3} ho v_{rms}^{2}$.From the ideal gas equation,$PV = nRT$,we have $P = \frac{nRT}{V}$.Since $n$,$R$,and $V$ are constant for a closed container,the pressure $P$ is directly proportional to the temperature $T$,i.e.,$P \propto T$.The force $F$ exerted on the walls is given by $F = P 	imes A$,where $A$ is the surface area of the wall.Since $A$ is constant for a closed container,$F \propto P$.Therefore,$F \propto T$,which implies $F \propto T^{1}$.Comparing this with $T^{x}$,we get $x = 1$.

The average force applied on the walls of a closed container depends as $T^{x}$ where $T$ is the temperature of an ideal gas. The value of $x$ is

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